Convex set

subset of an affine space that is closed under convex combinations

In Euclidean space, a region is a convex set if the following is true. For any two points inside the region, a straight line segment can be drawn. If every point on that segment is inside the region, then the region is convex.

A convex set
A non-convex set

The point is that a convex curve forms the boundary of a convex set. So, any shape which is concave, or has a hollow, cannot be a convex set.

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